Get rid of the surrounding Xenomorphs and find the stairs to the upper galleries. Eliminate further aliens. Pay attention, since most of them will moving on the ceiling. Don't let any of them surprise you; if needed, use your flashlight and the motion tracker.
Follow O'Neal. At the entrance to the control room you'll be once again forced to defend your ally. In this case, I'd suggest a weapon with high accuracy rate, trying to kill the Xenomorphs before they reach the gallery you're currently on.
Enter the control room as soon as O'Neal unlocks the door. Ignore the Xenomorphs visible behind the windshield, and check out the room to find a new Dog Tag (PFC S. Trubetskoy).
Once you've collected everything there is to collect in the control room, interact with the above terminal which controls the cargo bay door. This will prompt new cutscenes and the end of the mission.